碳的变奏：全新2D材料石墨勒烯 (Graphullerene)

碳是生命中不可或缺的元素，具有多种杂化方式（sp、sp²、sp³）。比如，石墨和金刚石这两种碳的同素异形体中，金刚石为sp³杂化，形成三维碳原子网络，而石墨则是sp²杂化，形成层状结构，层与层之间为范德华力相互作用。

从石墨中发现石墨烯被认为是凝聚态物理的一项重大突破，然而这些碳同素异形体都不是半导体。C₆₀分子形状类似足球，由六边形和五边形碳原子构成，通过sp²杂化与其三个最近的邻居形成键合。

最近的研究合成了Mg与C₆₀分子结合的二维六角形结构（Mg₄C₆₀)_n。去除Mg后形成了石墨勒烯（Graphullerene），其碳原子同时表现出sp²和sp³杂化，暗示了其亚稳定性。Mg原子的掺杂对结构的稳定性影响很大，但Mg原子在稳定结构中的作用及其对材料性能的影响仍有待确定。

来自以色列的本–古里安大学材料工程系的Guy Makov教授小组，采用从头算的方法，研究了石墨勒烯的力学和能量稳定性、原子结构、声子色散曲线和能带结构。他们的研究证明了石墨勒烯是一种亚稳态半导体，其结构由受应变的C₆₀分子通过共价键与邻近分子相连构成。

他们还研究测定了石墨勒烯的键长和振动谱，并与孤立C₆₀分子进行了对比，发现了石墨勒烯的特征振动信号。作者揭示了Mg原子的作用，指出加入Mg原子可以使结构的形成能从负值转为正值，增强结构的能量稳定性，并降低电子带隙。

Fig. 5 Phonon modes.

这些发现与实验观察一致，为进一步开发这类材料的技术应用和合成路线提供了更坚实的理论基础。该文近期发布于npj Computational Materials 9: 211 (2023)。

Fig. 6 The electronic density difference between graphullerene with and without Mg atoms.

Editorial Summary

Carbon, an essential element in life, exhibits various hybridizations (sp, sp², sp³) as seen in allotropes like graphite and diamond. Diamond, with sp³ hybridization, forms a three-dimensional carbon network, whereas the sp² hybridization of graphite creates layered structures held together by van der Waals forces. The discovery of graphene from graphite is a significant breakthrough in condensed matter physics. However, these carbon allotropes are not semiconductors. C₆₀molecules, resembling soccer balls made of hexagonal and pentagonal carbon atoms, are bonded through sp² hybridization. Recent studies synthesized a two-dimensional hexagonal structure (Mg₄C₆₀)_ncombining magnesium and C₆₀ molecules. Upon removing Mg, Graphullerene forms, displaying both sp² and sp³ hybridizations, suggesting meta-stability. The doping of Mg atoms significantly impacts the structural stability, yet their role in the stabilized structure and influence on material properties remains to be determined. 

Fig. 7 Electron density of bulk graphullerene.

A group led by Prof. Guy Makov from the Dept. of Materials Engineering, Ben-Gurion University of the Negev, Israel, utilized ab initio calculations to study the mechanical and energy stability, atomic structure, phonon dispersion curves, and band structure of graphullerene. Their research confirms graphullerene as a meta-stable semiconductor, structured by strained C₆₀ molecules covalently bonded to neighbors. They also determined the bond lengths and vibrational spectrum of graphullerene, compared them with isolated C₆₀molecules and identified a characteristic vibrational signature. Moreover, they revealed the role of Mg atoms, noting that their inclusion turns the formation energy from negative to positive, enhancing stability and reducing the electronic band gap. These findings align with experimental observations, laying a solid foundation for further technological applications and synthetic routes of such materials. This article was recently published in npj Computational Materials 9: 211 (2023).

原文Abstract及其翻译

Structure and properties of graphullerene: a semiconducting two-dimensional C₆₀ Crystal （graphullerene的结构和性质：一种半导体性的二维C₆₀ 晶体结构）

Uri Argaman & Guy Makov 

Abstract Graphullerene is a recently discovered, two-dimensional allotrope of carbon formed from C₆₀ molecules. It has been synthesized in the form (C₆₀Mg₄)_n and subsequently transformed into (C₆₀)_n by removal of the Mg atoms. Ab initio calculations are employed to examine the structure and properties of this material. Structurally, graphullerene is composed of strained C₆₀ molecules. Each of these molecules is connected to six neighbors in a hexagonal network with a total of eight chemical bonds. We find this structure to be meta-stable, owing to the strain produced by the covalent bonding of the molecules. However, the inclusion of Mg atoms transforms the cohesion energy from negative to positive values by forming additional C-Mg bonds, creating an energetically stable material. In the absence of Mg, this allotrope is a pure carbon semiconductor with an indirect band gap. Phonon spectrum calculations confirm the dynamical stability of the material and yield its in- and out-of-plane sound velocities. In addition, symmetry breaking of the C₆₀ molecules results in a distribution of bond lengths and creates vibrational modes that serve as a signature of graphullerene.

摘要Graphullerene是最近发现的一种碳的二维同素异形体，由C₆₀分子组成。它以(C₆₀Mg₄)_n的形式合成，随后通过去除镁原子转化为(C₆₀)_n。我们采用从头算计算方法来研究这种材料的结构和性质。从结构上看，石墨勒烯（Graphullerene）由受应力的C₆₀分子组成。每个分子都与六个相邻的分子形成六角形的网络，总共有八个化学键。我们发现这种结构是亚稳定的，这是由于分子间的共价键形成的应力导致的。然而，镁原子的存在通过形成额外的C-Mg键将结合能从负值转化为正值，从而创造出一个在能量上稳定的材料。在没有镁的情况下，这种同素异形体是一种纯碳半导体，具有间接带隙。声子谱确认了材料的动力学稳定性，并得出了其面内和面外声速。此外，C₆₀分子的对称性破缺导致键长分布的出现，并产生了作为石墨勒烯特征的振动模式。